Have you tried setting the default audio device to headphones, then load up Chrome, then set the default audio device to speakers, and load up Firefox. Does that work? If these applications select the audio device at load time it might do the trick.
If it does work, you could write a .bat file and use a program such as NirCmd (
http://www.nirsoft.net/utils/nircmd.html) to automate the audio device switching and browser loading.
For example:
@echo off
NirCmd.exe setdefaultsounddevice "Headphones"
start chrome
pause
NirCmd.exe setdefaultsounddevice "Speakers"
start firefox